The more precisely the position is determined, the less precisely
the momentum is known in this instant, and vice versa. --Heisenberg, uncertainty
paper, 1927

This is a succinct statement of the "uncertainty relation" between the position
and the momentum (mass times velocity) of a subatomic particle, such as an electron.
This relation has profound implications for such fundamental notions as causality
and the determination of the future behavior of an atomic particle.

Because of the scientific and philosophical implications of the seemingly harmless
sounding uncertainty relations, physicists speak of an uncertainty principle,
which is often called more descriptively the "principle of indeterminacy." This
page focuses on the origins of Heisenberg's uncertainty relations and principle.

To hear Heisenberg recall his early thoughts on the Uncertainty Principle,
click Sound Bites.

The origins of uncertainty entail almost as much personality as they do physics.
Heisenberg's route to uncertainty lies in a debate that began in early 1926
between Heisenberg and his closest colleagues on the one hand, who espoused
the "matrix" form of quantum mechanics, and Erwin Schrödinger and his colleagues
on the other, who espoused the new "wave mechanics."

I knew of [Heisenberg's] theory, of course, but I felt discouraged,
not to say repelled, by the methods of transcendental algebra, which appeared
difficult to me, and by the lack of visualizability. -Schrödinger in 1926

Most physicists were slow to accept "matrix mechanics" because of its abstract
nature and its unfamiliar mathematics. They gladly welcomed Schrödinger's alternative
wave mechanics when it appeared in early 1926, since it entailed more familiar
concepts and equations, and it seemed to do away with quantum jumps and discontinuities.
French physicist Louis de Broglie had suggested that not only light but also
matter might behave like a wave. Drawing on this idea, to which Einstein had
lent his support, Schrödinger attributed the quantum energies of the electron
orbits in the old quantum theory of the atom to
the vibration frequencies of electron "matter waves" around the atom's nucleus.
Just as a piano string has a fixed tone, so an electron-wave would have a fixed
quantum of energy. This led to much easier calculations and more familiar visualizations
of atomic events than did Heisenberg's matrix mechanics, where the energy was
found in an abstruse calculation.

I had no faith in a theory that ran completely counter to
our Copenhagen conception. --Heisenberg, recollection

In May 1926 Schrödinger published a proof that matrix and wave mechanics gave
equivalent results: mathematically they were the same theory. He also argued
for the superiority of wave mechanics over matrix mechanics. This provoked an
angry reaction, especially from Heisenberg, who insisted on the existence of
discontinuous quantum jumps rather than a theory based on continuous waves.

There was more at stake than personal preferences, for jobs were now in the
balance for the creators of matrix mechanics. Most of the young men who created
matrix mechanics were ready to move into teaching positions as professors, and
the older generation of theoretical physicists was beginning to vacate positions
at German universities. Heisenberg's family was exerting pressure on the young
man to capture one of the vacancies at the same time that his best work, matrix
mechanics, seemed to be overshadowed by wave mechanics.

The more I think about the physical portion of Schrödinger's
theory, the more repulsive I find it...What Schrödinger writes about the visualizability
of his theory 'is probably not quite right,' in other words it's crap. --Heisenberg,
writing to Pauli, 1926

Heisenberg had just begun his job as Niels Bohr's assistant in Copenhagen when
Schrödinger came to town in October 1926 to debate the alternative theories
with Bohr. The intense debates in Copenhagen proved inconclusive. They showed
only that neither interpretation of atomic events could be considered satisfactory.
Both sides began searching for a satisfactory physical interpretation of the
quantum mechanics equations in line with their own preferences.

After Schrödinger showed the equivalence of the matrix and wave versions of
quantum mechanics, and Born presented a statistical interpretation of the wave
function, Jordan in Göttingen and Paul Dirac in Cambridge, England, created
unified equations known as "transformation theory." These formed the basis of
what is now regarded as quantum mechanics. The task then became a search for
the physical meaning of these equations in actual situations showing the nature
of physical objects in terms of waves or particles, or both. As Bohr later explained
it, events in tiny atoms are subject to quantum mechanics, yet people deal with
larger objects in the laboratory, where the "classical" physics of Newton prevails.
What was needed was an "interpretation" of the Dirac-Jordan quantum equations
that would allow physicists to connect observations in the everyday world of
the laboratory with events and processes in the quantum world of the atom.

Studying the papers of Dirac and Jordan, while in frequent correspondence with
Wolfgang Pauli, Heisenberg discovered a problem in the way one could measure
basic physical variables appearing in the equations. His analysis showed that
uncertainties, or imprecisions, always turned up if one tried to measure the
position and the momentum of a particle at the same time. (Similar uncertainties
occurred when measuring the energy and the time variables of the particle simultaneously.)
These uncertainties or imprecisions in the measurements were not the fault of
the experimenter, said Heisenberg, they were inherent in quantum mechanics.
Heisenberg presented his discovery and its consequences in a 14-page letter
to Pauli in February 1927. The letter evolved into a published paper in which
Heisenberg presented to the world for the first time what became known as the
uncertainty principle.